Question: The sum of two numbers is $81$, and their difference is $33$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 81}$ ${x-y = 33}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 114 $ $ x = \dfrac{114}{2} $ ${x = 57}$ Now that you know ${x = 57}$ , plug it back into $ {x+y = 81}$ to find $y$ ${(57)}{ + y = 81}$ ${y = 24}$ You can also plug ${x = 57}$ into $ {x-y = 33}$ and get the same answer for $y$ ${(57)}{ - y = 33}$ ${y = 24}$ Therefore, the larger number is $57$, and the smaller number is $24$.